We propose the use of the Hermite interpolation polynomial in the Finite Element Method as an alternative to the vector finite element approach to solutions of Maxwell's equations. We analyzed the behavior of electromagnetic waves in waveguides. As with vector finite elements, we are able to suppress spurious solutions by appropriately setting the boundary conditions at interfaces. However with the derivative continuity provided by the quintic Hermite shape functions, we are able to provide greater accuracy than the vector finite element of equal polynomial order. Our scheme therefore has proven successful in calculations involving electromagnetic fields while at the same time providing better results than standard methods.
Worcester Polytechnic Institute
Major Qualifying Project
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